Given the equation below, determine two solutions such that $0 ^ { \circ }

Question

Given the equation below, determine two solutions such that $0 ^ { \circ } < \theta < 360 ^ { \circ }$ . 
cos $\theta$ = $- \frac { \sqrt { 3 } } { 2 }$
A)$\theta$ = 225 $^ { \circ }$ , 135 $^ { \circ }$
B)$\theta$= 135 $^ { \circ }$ , 225 $^ { \circ }$
C)$\theta$ = 150 $^ { \circ }$ , 210 $^ { \circ }$
D)$\theta$ = 300 $^ { \circ }$ , 240 $^ { \circ }$
E)$\theta$ = 30 $^ { \circ }$

Quizplus · Accepted Answer

The cosine of an angle is negative in the second and third quadrants, where the angles are 180° - θ and 180° + θ respectively. For cos(θ) = -√3/2, the reference angle θ is 30°, so the solutions are 180° - 30° = 150° and 180° + 30° = 210°.

Given the Equation Below, Determine Two Solutions Such That 0∘<θ<360∘0 ^ { \circ } < \theta < 360 ^ { \circ }0∘<θ<360∘

Given the Equation Below, Determine Two Solutions Such That $0 ^ { \circ } < \theta < 360 ^ { \circ }$